LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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subroutine checon_3 | ( | character | UPLO, |
integer | N, | ||
complex, dimension( lda, * ) | A, | ||
integer | LDA, | ||
complex, dimension( * ) | E, | ||
integer, dimension( * ) | IPIV, | ||
real | ANORM, | ||
real | RCOND, | ||
complex, dimension( * ) | WORK, | ||
integer | INFO | ||
) |
CHECON_3
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CHECON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian matrix A using the factorization computed by CHETRF_RK or CHETRF_BK: A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T), where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver CHETRS_3.
[in] | UPLO | UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = 'U': Upper triangular, form is A = P*U*D*(U**H)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**H)*(P**T). |
[in] | N | N is INTEGER The order of the matrix A. N >= 0. |
[in] | A | A is COMPLEX array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and CHETRF_BK: a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A. |
[in] | LDA | LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[in] | E | E is COMPLEX array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases. |
[in] | IPIV | IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHETRF_RK or CHETRF_BK. |
[in] | ANORM | ANORM is REAL The 1-norm of the original matrix A. |
[out] | RCOND | RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. |
[out] | WORK | WORK is COMPLEX array, dimension (2*N) |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value |
June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester